Subgroups — C₇×#22519 #13199735

Order 1792.

1086 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1991	C₂	1	2	yes	maximal, complemented
5	C₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1989	C₂	1	2	yes	maximal, complemented
7	C₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1804	C₂	1	2	yes	maximal
9	C₇×#1802	C₂	1	1	yes	maximal, characteristic
10	C₄×C₇×#102	C₂	1	2	yes	maximal
11	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic
12	C₇×#554	—	2	4	no	—
13	C₇×#554	C₄	1	8	yes	complemented
14	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×#125	C₂²	1	2	yes	—
16	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
21	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
22	C₇×C₈×Q₈	—	2	4	no	—
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₇×#102	C₂²	1	2	yes	—
26	C₂×C₇×#102	C₂²	1	1	yes	characteristic
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
30	C₇×#391	—	2	1	no	—
31	C₇×#387	—	2	2	no	—
32	C₇×#384	C₂²	1	1	yes	characteristic
33	C₇×#382	C₂²	1	2	yes	—
34	C₄×C₇×C₄⋊C₄	—	2	1	no	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
37	C₇×#340	C₂²	1	2	yes	—
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	1	yes	characteristic
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#340	C₂²	1	2	yes	—
43	C₇×#340	C₂²	1	1	yes	characteristic
44	#22519	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₇×Q₈	—	2	1	no	—
46	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
47	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₇	—	2	1	no	—
49	C₂³×C₄×C₇	—	2	2	no	—
50	C₂²×C₇×C₈	C₂³	1	2	yes	—
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₇×C₄⋊Q₈	—	2	2	no	—
54	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	—
55	C₇×#125	—	2	4	no	—
56	C₇×#125	C₂×C₄	1	8	yes	—
57	C₇×C₂²⋊Q₈	—	2	8	no	—
58	C₇×C₂²⋊Q₈	—	2	16	no	—
59	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
60	C₄×C₇×Q₈	D₄	1	4	yes	—
61	C₄×C₇×D₄	—	2	4	no	—
62	C₄×C₇×D₄	—	2	2	no	—
63	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
64	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
65	C₂×C₇×C₄⋊C₄	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	—	2	1	no	—
67	C₂×C₇×C₄⋊C₄	—	2	2	no	—
68	C₂×C₇×C₄⋊C₄	—	2	8	no	—
69	C₂×C₇×C₄⋊C₄	—	2	1	no	—
70	C₂×C₇×C₄⋊C₄	—	2	1	no	—
71	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₄²×C₇	—	2	1	no	—
81	C₂×C₄²×C₇	—	2	2	no	—
82	C₂×C₄²×C₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
84	C₇×C₄⋊C₈	—	2	4	no	—
85	C₇×C₄⋊C₈	—	2	2	no	—
86	C₇×#102	—	2	4	no	—
87	C₇×#102	—	2	2	no	—
88	C₇×#102	Q₈	1	4	yes	complemented
89	C₄×C₇×C₈	—	2	4	no	—
90	C₄×C₇×C₈	—	2	2	no	—
91	C₇×#95	—	2	2	no	—
92	C₇×#95	—	2	1	no	—
93	C₇×#95	—	2	2	no	—
94	C₇×#95	—	2	2	no	—
95	C₂×#554	C₂×C₇	1	1	yes	characteristic
96	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
97	#2355	C₂×C₇	1	1	yes	characteristic, complemented
98	#1991	C₂×C₇	1	2	yes	complemented
99	#1990	C₂×C₇	1	1	yes	characteristic, complemented
100	#1989	C₂×C₇	1	2	yes	complemented
101	#1987	C₂×C₇	1	1	yes	characteristic, complemented
102	#1804	C₂×C₇	1	2	yes	—
103	#1802	C₂×C₇	1	1	yes	characteristic
104	C₄×#102	C₂×C₇	1	1	yes	characteristic
105	C₄×#102	C₂×C₇	1	2	yes	—
106	C₂⁴×C₇	—	2	1	no	—
107	C₂×C₇×Q₈	—	2	4	no	—
108	C₂×C₇×Q₈	—	2	2	no	—
109	C₂×C₇×Q₈	—	2	2	no	—
110	C₂×C₇×Q₈	—	8	1	no	—
111	C₂×C₇×Q₈	—	8	1	no	—
112	C₂×C₇×Q₈	C₂²⋊C₄	1	4	yes	—
113	C₂×C₇×D₄	—	2	1	no	—
114	C₂×C₇×D₄	—	2	1	no	—
115	C₂×C₇×D₄	—	2	1	no	—
116	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
117	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
118	C₂×C₇×D₄	#41	1	2	yes	—
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	—	2	1	no	—
121	C₂²×C₄×C₇	—	2	2	no	—
122	C₂²×C₄×C₇	—	2	4	no	—
123	C₂²×C₄×C₇	—	2	8	no	—
124	C₂²×C₄×C₇	—	2	1	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	4	2	no	—
127	C₂²×C₄×C₇	—	4	2	no	—
128	C₂²×C₄×C₇	—	8	2	no	—
129	C₂²×C₄×C₇	—	8	2	no	—
130	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	2	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	2	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	2	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
144	C₇×C₄⋊C₄	—	2	8	no	—
145	C₇×C₄⋊C₄	—	2	4	no	—
146	C₇×C₄⋊C₄	—	2	8	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	2	no	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	2	1	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	1	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	4	2	no	—
155	C₇×C₄⋊C₄	—	8	1	no	—
156	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
157	C₇×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
158	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
159	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
160	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
161	C₇×C₂²⋊C₄	—	2	4	no	—
162	C₇×C₂²⋊C₄	—	2	8	no	—
163	C₄²×C₇	—	4	2	no	—
164	C₄²×C₇	—	8	2	no	—
165	C₄²×C₇	C₂²×C₄	1	4	yes	—
166	C₄²×C₇	C₂²×C₄	1	2	yes	—
167	C₄²×C₇	C₂×D₄	1	4	yes	—
168	C₄²×C₇	C₂×D₄	1	2	yes	—
169	#554	—	2	4	no	—
170	#554	C₄×C₇	1	8	yes	complemented
171	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
172	C₂×#125	C₂²×C₇	1	2	yes	—
173	C₂×C₂²⋊Q₈	—	2	1	no	—
174	C₂×C₂²⋊Q₈	—	2	2	no	—
175	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
176	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
178	C₂²×C₄⋊C₄	—	2	1	no	—
179	C₈×Q₈	—	2	4	no	—
180	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
181	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
182	C₂×#102	C₂²×C₇	1	2	yes	—
183	C₂×#102	C₂²×C₇	1	1	yes	characteristic
184	C₂×#102	C₂²×C₇	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
187	#391	—	2	1	no	—
188	#387	—	2	2	no	—
189	#384	C₂²×C₇	1	1	yes	characteristic
190	#382	C₂²×C₇	1	2	yes	—
191	C₄×C₄⋊C₄	—	2	1	no	—
192	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
193	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
194	#340	C₂²×C₇	1	2	yes	—
195	#340	C₂²×C₇	1	2	yes	—
196	#340	C₂²×C₇	1	2	yes	—
197	#340	C₂²×C₇	1	2	yes	—
198	#340	C₂²×C₇	1	1	yes	characteristic
199	#340	C₂²×C₇	1	2	yes	—
200	#340	C₂²×C₇	1	1	yes	characteristic
201	C₂³×C₇	—	2	2	no	—
202	C₂³×C₇	—	2	2	no	—
203	C₂³×C₇	—	2	2	no	—
204	C₂³×C₇	—	4	1	no	—
205	C₂³×C₇	—	4	1	no	—
206	C₂³×C₇	—	4	1	no	—
207	C₂³×C₇	—	4	1	no	—
208	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
209	C₇×Q₈	—	2	8	no	—
210	C₇×Q₈	—	8	4	no	—
211	C₇×D₄	—	2	2	no	—
212	C₇×D₄	—	2	2	no	—
213	C₇×D₄	—	2	2	no	—
214	C₇×D₄	C₄×Q₈	1	4	yes	—
215	C₂×C₄×C₇	—	2	2	no	—
216	C₂×C₄×C₇	—	2	2	no	—
217	C₂×C₄×C₇	—	2	2	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	2	4	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	1	no	—
227	C₂×C₄×C₇	—	4	1	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	4	8	no	—
231	C₂×C₄×C₇	—	4	1	no	—
232	C₂×C₄×C₇	—	4	2	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	4	2	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	4	1	no	—
237	C₂×C₄×C₇	—	8	8	no	—
238	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	4	yes	—
239	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
240	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	4	yes	—
241	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂×C₄×C₇	#135	1	2	yes	—
243	C₂×C₄×C₇	#135	1	2	yes	—
244	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
249	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
250	C₇×C₈	—	2	2	no	—
251	C₇×C₈	—	4	2	no	—
252	C₇×C₈	—	4	1	no	—
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
255	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	—	2	2	no	—
258	C₂²×C₈	C₂³×C₇	1	2	yes	—
259	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	—
263	#125	—	2	4	no	—
264	#125	C₂×C₄×C₇	1	8	yes	—
265	C₂²⋊Q₈	—	2	8	no	—
266	C₂²⋊Q₈	—	2	16	no	—
267	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
268	C₄×Q₈	C₇×D₄	1	4	yes	—
269	C₄×D₄	—	2	4	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
272	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	8	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂³×C₇	1	2	yes	—
291	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
292	C₄⋊C₈	—	2	4	no	—
293	C₄⋊C₈	—	2	2	no	—
294	#102	—	2	4	no	—
295	#102	—	2	2	no	—
296	#102	C₇×Q₈	1	4	yes	complemented
297	C₄×C₈	—	2	4	no	—
298	C₄×C₈	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	C₂²×C₇	—	2	4	no	—
304	C₂²×C₇	—	4	2	no	—
305	C₂²×C₇	—	4	2	no	—
306	C₂²×C₇	—	4	2	no	—
307	C₂²×C₇	—	4	2	no	—
308	C₂²×C₇	—	4	2	no	—
309	C₂²×C₇	—	4	2	no	—
310	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
311	C₂²×C₇	#548	1	1	yes	characteristic
312	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
313	C₂²×C₇	C₂×#135	1	1	yes	characteristic
314	C₂²×C₇	C₂×#135	1	1	yes	characteristic
315	C₂²×C₇	#576	1	1	yes	characteristic
316	C₂²×C₇	#577	1	1	yes	characteristic
317	C₄×C₇	—	2	4	no	—
318	C₄×C₇	—	2	4	no	—
319	C₄×C₇	—	2	2	no	—
320	C₄×C₇	—	4	2	no	—
321	C₄×C₇	—	4	2	no	—
322	C₄×C₇	—	4	4	no	—
323	C₄×C₇	—	8	1	no	—
324	C₄×C₇	—	8	2	no	—
325	C₄×C₇	#416	1	4	yes	—
326	C₄×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
327	C₄×C₇	#519	1	1	yes	characteristic
328	C₄×C₇	#548	1	1	yes	characteristic
329	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
330	C₂⁴	—	2	1	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	8	1	no	—
335	C₂×Q₈	—	8	1	no	—
336	C₂×Q₈	C₇×C₂²⋊C₄	1	4	yes	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
341	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
342	C₂×D₄	C₇×#41	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	8	2	no	—
353	C₂²×C₄	—	8	2	no	—
354	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
355	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
356	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	8	1	no	—
380	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
381	C₄⋊C₄	C₇×C₂²⋊C₄	1	8	yes	—
382	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
383	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
384	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₄²	—	4	2	no	—
388	C₄²	—	8	2	no	—
389	C₄²	C₂²×C₄×C₇	1	4	yes	—
390	C₄²	C₂²×C₄×C₇	1	2	yes	—
391	C₄²	C₂×C₇×D₄	1	4	yes	—
392	C₄²	C₂×C₇×D₄	1	2	yes	—
393	C₂×C₇	—	4	4	no	—
394	C₂×C₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
395	C₂×C₇	C₂×#416	1	1	yes	characteristic
396	C₂×C₇	#2897	1	1	yes	characteristic
397	C₂×C₇	#3360	1	1	yes	characteristic
398	C₂×C₇	#3361	1	1	yes	characteristic
399	C₂×C₇	#3380	1	1	yes	characteristic
400	C₂×C₇	#3381	1	1	yes	characteristic
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
409	Q₈	—	2	8	no	—
410	Q₈	—	8	4	no	—
411	D₄	—	2	2	no	—
412	D₄	—	2	2	no	—
413	D₄	—	2	2	no	—
414	D₄	C₄×C₇×Q₈	1	4	yes	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	8	8	no	—
438	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	4	yes	—
439	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
440	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	4	yes	—
441	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
442	C₂×C₄	C₇×#135	1	2	yes	—
443	C₂×C₄	C₇×#135	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
445	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
447	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
448	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
449	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	4	2	no	—
452	C₈	—	4	1	no	—
453	C₇	#22519	1	1	yes	characteristic, direct product factor, Sylow
454	C₂²	—	2	4	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
462	C₂²	C₇×#548	1	1	yes	characteristic
463	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
464	C₂²	C₂×C₇×#135	1	1	yes	characteristic
465	C₂²	C₂×C₇×#135	1	1	yes	characteristic
466	C₂²	C₇×#576	1	1	yes	characteristic
467	C₂²	C₇×#577	1	1	yes	characteristic
468	C₄	—	2	4	no	—
469	C₄	—	2	4	no	—
470	C₄	—	2	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	4	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	2	no	—
476	C₄	C₇×#416	1	4	yes	—
477	C₄	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
478	C₄	C₇×#519	1	1	yes	characteristic
479	C₄	C₇×#548	1	1	yes	characteristic
480	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
481	C₂	—	4	4	no	—
482	C₂	C₇×Q₈×C₂²⋊C₄	1	1	yes	characteristic
483	C₂	C₂×C₇×#416	1	1	yes	characteristic
484	C₂	C₇×#2897	1	1	yes	characteristic
485	C₂	C₇×#3360	1	1	yes	characteristic
486	C₂	C₇×#3361	1	1	yes	characteristic
487	C₂	C₇×#3380	1	1	yes	characteristic
488	C₂	C₇×#3381	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₇×C₈×Q₈	C₂	semidirect
3. C₇×#2355	C₂	semidirect
4. C₇×#1991	C₂	semidirect
5. C₇×#1990	C₂	semidirect
6. C₇×#1989	C₂	semidirect
7. C₇×#1987	C₂	semidirect
13. C₇×#554	C₄	semidirect
44. #22519	C₇	direct (N × H)
88. C₇×#102	Q₈	semidirect
96. C₂×C₈×Q₈	C₂×C₇	semidirect
97. #2355	C₂×C₇	semidirect
98. #1991	C₂×C₇	semidirect
99. #1990	C₂×C₇	semidirect
100. #1989	C₂×C₇	semidirect
101. #1987	C₂×C₇	semidirect
170. #554	C₄×C₇	semidirect
296. #102	C₇×Q₈	semidirect
453. C₇	#22519	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#554	2
C₂×C₇×C₈×Q₈	2
C₇×#2355	2
C₇×#1991	2
C₇×#1990	2
C₇×#1989	2
C₇×#1987	2
C₇×#1804	2
C₇×#1802	2
C₄×C₇×#102	2
#22519	7

Subgroups — C7×#22519 #13199735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22519 #13199735